A generalization of the Kostka-Foulkes polynomials

Abstract

Combinatorial objects called rigged configurations give rise to q-analogues of certain Littlewood-Richardson coefficients. The Kostka-Foulkes polynomials and two-column Macdonald-Kostka polynomials occur as special cases. Conjecturally these polynomials coincide with the Poincare polynomials of isotypic components of certain graded GL(n)-modules supported in a nilpotent conjugacy class closure in gl(n).

arXiv comment37 pages

Cited by in corpus (10)

• Inhomogeneous lattice paths, generalized Kostka polynomials and A${}_{n-1}$ supernomials
• Character Formulae of ${\widehat{sl}}_n$-Modules and Inhomogeneous Paths
• Cylindric versions of specialised Macdonald functions and a deformed Verlinde algebra
• Affine type A crystal structure on tensor products of rectangles, Demazure characters, and nilpotent varieties
• Rigged configuration bijection and proof of the $X=M$ conjecture for nonexceptional affine types
• Ubiquity of Kostka polynomials
• A cyclage poset structure for Littlewood-Richardson tableaux
• Graded characters of modules supported in the closure of a nilpotent conjugacy class
• A q-analog of Schur's Q-functions
• Multi-atoms and monotonicity of generalized Kostka polynomials